Zeolites for the selective adsorption of sulfur hexafluoride.

Molecular simulations have been used to investigate at the molecular level the suitability of zeolites with different topology on the adsorption, diffusion and separation of a nitrogen-sulfur hexafluoride mixture containing the latter at low concentration. This mixture represents the best alternative for the sulfur hexafluoride in industry since it reduces the use of this powerful greenhouse gas. A variety of zeolites are tested with the aim to identify the best structure for the recycling of sulfur hexafluoride in order to avoid its emission to the atmosphere and to overcome the experimental difficulties of its handling. Even though all zeolites show preferential adsorption of sulfur hexafluoride, we identified local structural features that reduce the affinity for sulfur hexafluoride in zeolites such as MOR and EON, providing exclusive adsorption sites for nitrogen. Structures such as ASV and FER were initially considered as good candidates based on their adsorption features. However, they were further discarded based on their diffusion properties. Regarding operation conditions for separation, the range of pressure that spans from 3 × 10(2) to 3 × 10(3) kPa was identified as the optimal to obtain the highest adsorption loading and the largest SF6/N2 selectivity. Based on these findings, zeolites BEC, ITR, IWW, and SFG were selected as the most promising materials for this particular separation.

Zeolite screening for the separation of gas mixtures containing SO2, CO2 and CO.

We used a combination of experiments and molecular simulations to investigate at the molecular level the effects of zeolite structure on the adsorption and diffusion of sulfur dioxide, carbon dioxide and carbon monoxide as well as separation processes of their mixtures. Our study involved different zeolite topologies and revealed numerous structure-property trends depending on the temperature and pressure conditions. Sulfur dioxide, which has the strongest interactions with zeolites due to its size and polarity, showed the largest adsorption across investigated temperatures and pressures. Our results indicate that structures with channel-type pore topology and low pore volume are the most promising for selective adsorption of sulfur dioxide over carbon dioxide and carbon monoxide under room conditions, while structures with higher pore volume exhibit better storage capacity at higher pressure. Our results emphasize the need for considering both adsorption and diffusion processes in the selection of the optimal structure for a given separation process. Our findings help to identify the best materials for effective separation processes under realistic operating conditions.

FSI Analysis of a healthy and a stenotic human trachea under impedance-based boundary conditions.

In this work, a fluid-solid interaction (FSI) analysis of a healthy and a stenotic human trachea was studied to evaluate flow patterns, wall stresses, and deformations under physiological and pathological conditions. The two analyzed tracheal geometries, which include the first bifurcation after the carina, were obtained from computed tomography images of healthy and diseased patients, respectively. A finite element-based commercial software code was used to perform the simulations. The tracheal wall was modeled as a fiber reinforced hyperelastic solid material in which the anisotropy due to the orientation of the fibers was introduced. Impedance-based pressure waveforms were computed using a method developed for the cardiovascular system, where the resistance of the respiratory system was calculated taking into account the entire bronchial tree, modeled as binary fractal network. Intratracheal flow patterns and tracheal wall deformation were analyzed under different scenarios. The simulations show the possibility of predicting, with FSI computations, flow and wall behavior for healthy and pathological tracheas. The computational modeling procedure presented herein can be a useful tool capable of evaluating quantities that cannot be assessed in vivo, such as wall stresses, pressure drop, and flow patterns, and to derive parameters that could help clinical decisions and improve surgical outcomes.

FSI analysis of a human trachea before and after prosthesis implantation.

In this work we analyzed the response of a stenotic trachea after a stent implantation. An endotracheal stent is the common treatment for tracheal diseases such as stenosis, chronic cough, or dispnoea episodes. Medical treatment and surgical techniques are still challenging due to the difficulties in overcoming potential complications after prosthesis implantation. A finite element model of a diseased and stented trachea was developed starting from a patient specific computerized tomography (CT) scan. The tracheal wall was modeled as a fiber reinforced hyperelastic material in which we modeled the anisotropy due to the orientation of the collagen fibers. Deformations of the tracheal cartilage rings and of the muscular membrane, as well as the maximum principal stresses, are analyzed using a fluid solid interaction (FSI) approach. For this reason, as boundary conditions, impedance-based pressure waveforms were computed modeling the nonreconstructed vessels as a binary fractal network. The results showed that the presence of the stent prevents tracheal muscle deflections and indicated a local recirculatory flow on the stent top surface which may play a role in the process of mucous accumulation. The present work gives new insight into clinical procedures, predicting their mechanical consequences. This tool could be used in the future as preoperative planning software to help the thoracic surgeons in deciding the optimal prosthesis type as well as its size and positioning.

Numerical simulation of bone remodelling around dental implants.

Crestal bone loss can result in the failure of dental implants and can be caused, by among other factors, the development of non-physiological mechanical conditions. Bone remodelling (BR) is the physiological process through which bone adapts itself to the mechanical environment. A previously published mathematical model of BR is used in this work to study the homogenized structural evolution of peri-implant bone. This model is used to study the influence of the diameter and length of a dental implant of pure titanium on its long-term stability. The temporal evolution of porosity and microstructural damage of the peri-implant bone are the variables analysed in this study. The results show that damage and porosity increase as the implant length decreases and, more pronouncedly, as its diameter decreases. The increase in damage and porosity levels is localized, as many other studies confirm, at the implant neck due to the stress concentration that is created in that area. The main conclusion of this study is that in implants with a diameter equal to or greater than 3 mm the damage is under control and there is no mechanical failure of the peri-implant bone in the long term.

Data-Driven Computational Simulation in Bone Mechanics.

The data-driven approach was formally introduced in the field of computational mechanics just a few years ago, but it has gained increasing interest and application as disruptive technology in many other fields of physics and engineering. Although the fundamental bases of the method have been already settled, there are still many challenges to solve, which are often inherently linked to the problem at hand. In this paper, the data-driven methodology is applied to a particular problem in tissue biomechanics, a context where this approach is particularly suitable due to the difficulty in establishing accurate and general constitutive models, due to the intrinsic intra and inter-individual variability of the microstructure and associated mechanical properties of biological tissues. The problem addressed here corresponds to the characterization and mechanical simulation of a piece of cortical bone tissue. Cortical horse bone tissue was mechanically tested using a biaxial machine. The displacement field was obtained by means of digital image correlation and then transformed into strains by approximating the displacement derivatives in the bone virtual geometric image. These results, together with the approximated stress state, assumed as uniform in the small pieces tested, were used as input in the flowchart of the data-driven methodology to solve several numerical examples, which were compared with the corresponding classical model-based fitted solution. From these results, we conclude that the data-driven methodology is a useful tool to directly simulate problems of biomechanical interest without the imposition (model-free) of complex spatial and individually-varying constitutive laws. The presented data-driven approach recovers the natural spatial variation of the solution, resulting from the complex structure of bone tissue, i.e. heterogeneity, microstructural hierarchy and multifactorial architecture, making it possible to add the intrinsic stochasticity of biological tissues into the data set and into the numerical approach.

On the modelling of biological patterns with mechanochemical models: Insights from analysis and computation.

The diversity of biological form is generated by a relatively small number of underlying mechanisms. Consequently, mathematical and computational modelling can, and does, provide insight into how cellular level interactions ultimately give rise to higher level structure. Given cells respond to mechanical stimuli, it is therefore important to consider the effects of these responses within biological self-organisation models. Here, we consider the self-organisation properties of a mechanochemical model previously developed by three of the authors in Acta Biomater. 4, 613-621 (2008), which is capable of reproducing the behaviour of a population of cells cultured on an elastic substrate in response to a variety of stimuli. In particular, we examine the conditions under which stable spatial patterns can emerge with this model, focusing on the influence of mechanical stimuli and the interplay of non-local phenomena. To this end, we have performed a linear stability analysis and numerical simulations based on a mixed finite element formulation, which have allowed us to study the dynamical behaviour of the system in terms of the qualitative shape of the dispersion relation. We show that the consideration of mechanotaxis, namely changes in migration speeds and directions in response to mechanical stimuli alters the conditions for pattern formation in a singular manner. Furthermore without non-local effects, responses to mechanical stimuli are observed to result in dispersion relations with positive growth rates at arbitrarily large wavenumbers, in turn yielding heterogeneity at the cellular level in model predictions. This highlights the sensitivity and necessity of non-local effects in mechanically influenced biological pattern formation models and the ultimate failure of the continuum approximation in their absence.

An interspecies computational study on limb lengthening.

Distraction osteogenesis is a surgical technique that produces large volumes of new bone by gradually separating two osteotomized bone segments. A previously proposed mechanical-based model that includes the effect of pre-traction stresses (stress level in the gap tissue before each distraction step) during limb lengthening is used here. In the present work, the spatial and temporal patterns of tissue distribution during distraction osteogenesis in different species (sheep, rabbit) and in the human are compared numerically to predict experimental results. Interspecies differential characteristics such as size, distraction protocol, and rate of distraction, among others, are chosen according to experiments. Tissue distributions and reaction forces are then analysed as indicators of the healing pattern. The results obtained are in agreement with experimental findings regarding both tissue distribution and reaction forces. The ability of the model to qualitatively predict the two animal models and the human healing pattern in distraction osteogenesis indicates its potential in understanding the influence of mechanics in this complex process.

On the role of bone damage in calcium homeostasis.

Bone serves as the reservoir of some minerals including calcium. If calcium is needed anywhere in the body, it can be removed from the bone matrix by resorption and put back into the blood flow. During bone remodelling the resorbed tissue is replaced by osteoid which gets mineralized very slowly. Then, calcium homeostasis is controlled by bone remodelling, among other processes: the more intense is the remodelling activity, the lower is the mineral content of bone matrix. Bone remodelling is initiated by the presence of microstructural damage. Some experimental evidences show that the fatigue properties of bone are degraded and more microdamage is accumulated due to the external load as the mineral content increases. That damage initiates bone remodelling and the mineral content is so reduced. Therefore, this process prevents the mineral content of bone matrix to reach very high (non-physiological) values. A bone remodelling model has been used to simulate this regulatory process. In this model, damage is an initiation factor for bone remodelling and is estimated through a fatigue algorithm, depending on the macroscopic strain level. Mineral content depends on bone remodelling and mineralization rate. Finally, the bone fatigue properties are defined as dependent on the mineral content, closing the interconnection between damage and mineral content. The remodelling model was applied to a simplified example consisting of a bar under tension with an initially heterogeneous mineral distribution. Considering the fatigue properties as dependent on the mineral content, the mineral distribution tends to be homogeneous with an ash fraction within the physiological range. If such dependance is not considered and fatigue properties are assumed constant, the homogenization is not always achieved and the mineral content may rise up to high non-physiological values. Thus, the interconnection between mineral content and fatigue properties is essential for the maintenance of bone's structural integrity as well as for the calcium homeostasis.

Modelling adaptative volumetric finite growth in patient-specific residually stressed arteries.

Understanding the functional performance of vascular tissue is taking a rising importance due to the increasing impact of cardiovascular diseases in developed countries. Currently available medical imaging acquisition techniques, combined with computer modelling allow patient-specific simulations of customized geometries that may help in medical diagnosis and therapeutic treatment. In this work we show methodology to develop patient-specific simulations. Particular features of arteries such as their multilayered structure, as well as the non-linear behaviour of the arterial tissue are considered. A strategy based on the decomposition of the deformation gradient tensor is followed in order to include residual stresses in the real geometry. By means of this technique, it is also possible to model the adaptative growth of the artery neglecting the developing process from the embryo state.

On modelling nonlinear viscoelastic effects in ligaments.

Experiments in human ligaments revealed that the rate of stress relaxation in such materials is strain dependent. This nonlinear behavior requires therefore a modified description of the standard quasilinear viscoelasticity theory commonly used in tissue biomechanics. The goal of this study is to characterize and demonstrate the importance of the nonlinear stress-relaxation behavior of ligaments undergoing finite deformation. The structural model presented herein is based on a local additive decomposition of the stress tensor into initial and non-equilibrium parts as resulted from the assumed structure of the free energy density function that generalizes Kelvin-Voigt nonlinear viscous models. We consider different viscoelastic behavior for the matrix and the fibers and the need of considering the strain dependency of this effect is clearly demonstrated. Model parameters were fit to experimental data obtained in specimens undergoing finite deformation in two directions: longitudinal and transversal with respect to the directions of the collagen fibers. The model was then tested against several multi-axial loading situations. The strain dependent relaxation and the strain rate dependent behavior of the human medial collateral ligament were accurately predicted.

An accurate finite element model of the cervical spine under quasi-static loading.

Cervical disc injury due to impact has been observed in clinical and biomechanical investigations; however, there is a lack of data that helps to elucidate the mechanisms of disc injury during these collisions. Therefore, it is necessary to understand the behavior of the cervical spine under different types of loading situations. A three dimensional finite element (FE) model for the multi-level cervical spine segment (C0-C7) was developed using computed tomography (CT) data and applied to study the internal stresses and strains of the intervertebral discs under quasi-static loading conditions. The intervertebral discs were treated as nonlinear, anisotropic and incompressible subjected to large deformations. The model accuracy was validated by comparing it with previously published experimental and numerical results for different movements. It was shown that the use of a fiber reinforced model to describe the behavior of the annulus of the discs would predict higher maximum shear strains than an isotropic one, being therefore important the use of complex constitutive models in order to be able to detect the appearance of injured zones, since those strains and stresses are supposed to be related with damage to soft tissues. Several movements were analyzed: flexion, extension and axial rotation, obtaining that the maximum shear stresses in the disc were higher for a flexo-extension movement.

Experimental study and constitutive modelling of the passive mechanical properties of the ovine infrarenal vena cava tissue.

The passive mechanical properties of the ovine infrarenal vena cava are analysed in this paper. In vivo stretch from 15 venae was measured in order to get data from the physiological situation before harvesting the vessel. Vena cava strips (n=64) both in longitudinal and circumferential directions were cut and subjected to simple tension tests. Results showed the strongly marked anisotropic character of the caval tissue. The maximal stretch ranges reached in both directions were very different, with the longitudinal range being much higher than the circumferential range in all cases. Three anisotropic constitutive models were used to fit the data obtained from the experiments. Advantages and drawbacks of each of these models are also discussed.

Computational simulation of dental implant osseointegration through resonance frequency analysis.

The aim of this study is to predict the evolution of the resonance frequency of the bone-implant interface in a dental implant by means of finite element simulation. A phenomenological interface model able to simulate the mechanical effects of the osseointegration process at the bone-implant interface is applied and compared with some experimental results in rabbits. An early stage of slow bone ingrowth, followed by a faster osseointegration phase until final stability is predicted by the simulations. The evolution of the resonance frequency of the implant and surrounding tissues along the simulation period was also obtained, observing a 3-fold increase in the first principal frequency. These findings are in quantitative agreement with the experimental measurements and suggest that the model can be useful to evaluate the influence of mechanical factors such as implant geometry or implant loading on the indirect evaluation of the process of implant osseintegration.

An experimental study of the mouse skin behaviour: damage and inelastic aspects.

Samples of male and female mice skin were tested under monotonic and cyclic loading to mechanically characterize the tissue for large deformations. Cyclic tests have shown a typical Mullins effect widely known for elastomers and other soft tissues. No statistical difference was found in the maximum stretch of the sample after the fifth loading cycle for male (1.26 +/- 0.035) and female (1.18 +/- 0.083). However, larger dispersion was obtained for the maximum stress for both genders, 0.61 +/- 0.16 MPa for male and 0.78 +/- 0.32 MPa for female. Results show the presence of inelastic strain and stress softening in the skin at large deformations. They also have shown how stress softening and residual strain change with the magnitude of the applied load. Good correlation was observed between the residual strain and the maximum strain previously attained by the sample during loading for all samples. However, the correlation was different between genders.

Dynamic 3D FE modelling of the human temporomandibular joint during whiplash.

Rear-end impacts account for more than one-third of vehicle accidents, and nearly 40% of these accidents produce whiplash injuries. Whiplash injury to the neck has often been considered a significant risk factor for the development of temporomandibular disorders (TMD). The objective of this study was to simulate the dynamic response of the temporomandibular joint during two types of impacts: a rear end and a frontal impact. To understand the dynamic forces acting on the joint, we extended a previous human temporomandibular joint model and analyzed the stress distributions in the soft elements of the joint. In the rear-end impact, it could be appreciated that the inertia of the mandible caused it to move posteriorly slower than the head, and this resulted in downward and forward displacements of the disc-condyle complex relative to the cranial base. Consequently, a rapid and big mouth opening occurs. In contrast, during the frontal impact, the mouth hardly opened, because the superior maxilla pushed the mandible to move together. There was not differential movement between bony components of the joint and therefore the soft tissues of the joint were not subjected to high loads. From these results, and despite the limitations of the simulations performed, we could conclude that neither a rear-end impact at low-velocity nor a frontal impact would produce damage to the soft tissues of the joint.

A finite element model to accurately predict real deformations of the breast.

Most surgical procedures in breast plastic surgery are either reconstructive procedures following oncologic interventions (tumorectomy, quadrantectomy, mastectomy ...) or aesthetic ones, both augmentation and reduction. With current techniques, the results of such procedures cannot be fully guaranteed. Usually, surgical planning is based on a photographic and anthropometric study of the breast only. Among others, one of the difficulties that the plastic surgeons have is the noticeable change of the breast shape with the position of the patient. Thus, it is more and more necessary to plan a presurgical methodology to help the plastic surgeon and guarantee the patient a successful result of the intervention. In order to establish a reliable simulation method that could predict a patient-specific outcome after breast surgery, this study started trying to correlate spatial features of the breast between lying and standing up positions. A biomechanical model of breast was proposed and implemented into a finite element context to predict deformations, and from these the breast shape in different positions. The resulting shapes were compared with multimodal images, whereas the breast surface displacements were compared with manually identified landmarks and 3D scanner images. From the results, it can be concluded that the model hereby presented reasonably approximates breast response to gravity forces, therefore providing accurate and useful information to the surgeon planning such surgical procedures.

Computer simulation of damage on distal femoral articular cartilage after meniscectomies.

It is commonly accepted that total or partial meniscectomies cause wear of articular cartilages that leads to severe damage in a period of few years. This also produces alteration of the biomechanical environment and increases articular instability, with a progressive and degenerative arthrosic pathology. Due to these negative consequences, total meniscectomy technique has been avoided, with a clear preference for partial meniscectomies. Despite the better results obtained with this latter technique, it has been demonstrated that the knee still suffers progressive long-term wear, which alters the properties of the surface of articular cartilage. In this paper, a phenomenological isotropic damage model of articular cartilage is presented and implemented in a finite element code. We hypothesized that there is a relation between the increase of shear stress and cartilage degeneration. To confirm the hypothesis, the obtained results were compared to experimental ones. It is used to investigate the effect of meniscectomies on articular damage in the human knee joint. Two different situations were compared for the tibio-femoral joint: healthy and after meniscectomy. The distribution of damaged regions and the damage level distribution resulted qualitatively similar to experimental results, showing, for instance that, after meniscectomy, significant degeneration occurs in the lateral compartment. A noteworthy result was that patterns of damage in a total meniscectomy model give better agreement to clinical results when using relative increases in shear stress, rather than an absolute shear stress criterion. The predictions for partial meniscectomies indicated the relative severity of the procedures.

Numerical estimation of bone density and elastic constants distribution in a human mandible.

In this paper, we try to predict the distribution of bone density and elastic constants in a human mandible, based on the stress level produced by mastication loads using a mathematical model of bone remodelling. These magnitudes are needed to build finite element models for the simulation of the mandible mechanical behavior. Such a model is intended for use in future studies of the stability of implant-supported dental prostheses. Various models of internal bone remodelling, both phenomenological and more recently mechanobiological, have been developed to determine the relation between bone density and the stress level that bone supports. Among the phenomenological models, there are only a few that are also able to reproduce the level of anisotropy. These latter have been successfully applied to long bones, primarily the femur. One of these models is here applied to the human mandible, whose corpus behaves as a long bone. The results of bone density distribution and level of anisotropy in different parts of the mandible have been compared with various clinical studies, with a reasonable level of agreement.

Computational simulation of fracture healing: influence of interfragmentary movement on the callus growth.

Bone fractures heal through a complex process involving several cellular events. This healing process can serve to study factors that control tissue growth and differentiation from mesenchymal stem cells. The mechanical environment at the fracture site is one of the factors influencing the healing process and controls size and differentiation patterns in the newly formed tissue. Mathematical models can be useful to unravel the complex relation between mechanical environment and tissue formation. In this study, we present a mathematical model that predicts tissue growth and differentiation patterns from local mechanical signals. Our aim was to investigate whether mechanical stimuli, through their influence on stem cell proliferation and chondrocyte hypertrophy, predict characteristic features of callus size and geometry. We found that the model predicted several geometric features of fracture calluses. For instance, callus size was predicted to increase with increasing movement. Also, increases in size were predicted to occur through increase in callus diameter but not callus length. These features agree with experimental observations. In addition, spatial and temporal tissue differentiation patterns were in qualitative agreement with well-known experimental results. We therefore conclude that local mechanical signals can probably explain the shape and size of fracture calluses.